Cable-driven continuum robots hold significant application value in environments such as space maintenance and equipment monitoring. This paper presents a novel structural design for a continuum robot. The robot's joint section comprises two interlinked quaternion joints, while the control drive box is simplified to a design where a single motor drives two cables. This design not only reduces the number of motors used but also enhances the smoothness of the arm's curvature. The designed linkage quaternion joint underwent kinematic analysis and cable decoupling calculation analysis to ensure the robot's motion accuracy and control efficiency. Based on this design, experiments were performed with a ten-degree-of-freedom prototype robot, including tests for navigating narrow pipelines, handling loads, and assessing repeatability in positioning accuracy. The experimental results demonstrate that the robot exhibits reliability and precision in complex operational environments.